System

We can eliminate y by subtracting the first and second equations and add the second and third equations.

So we have two equations and two variables now:

4x+2z=-12

-3x-z=9

Now we can use the elimination method to eliminate z by multiplying the bottom equation by 2 and adding it with the bottom.

-2x=6 x=-3

so now we know z=0 by substituting x into the previous equation.

similarly, we can find that y=1 by substituting x and z into any of the orig equations

Hope this helps